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Lipstick case is the name of outer foreskin of a mammal (especially a dog). It is different from just the "lipstick" (the exposed penis). The "lipstick case" can always be viewed while the animal is un-erect (like if sleeping). When the penis becomes erect, the lipstick case is considered to be open.
When the dog has an erection: "Look honey, the dog has his Lipstick case open"
or "Look sweety! the dog has his lispstick out of it's case!"

When the dog begins licking it: "Look sweetums, the dog is putting on his lipstick to!"
by logicmoo June 25, 2012